The ratio of milk and water in a pot is `3:4.` If 3l water is added, then the ratio becomes `3:5.` Find the initial quantity of milk.

Options

A. 8 litre
B. 5 litre
C. 9 litre
D. 12 litre

Answer

To solve the problem step by step, let's break it down:

**Step 1: Understand the initial ratio of milk and water.**
The initial ratio of milk to water is given as 3:4. This means that for every 3 parts of milk, there are 4 parts of water.

**Step 2: Define variables for milk and water.**
Let the initial quantity of milk be \( 3x \) liters and the initial quantity of water be \( 4x \) liters, where \( x \) is a common multiplier.

**Step 3: Add the additional water.**
According to the problem, 3 liters of water is added. Therefore, the new quantity of water becomes:
\[ 4x + 3 \text{ liters} \]

**Step 4: Set up the new ratio.**
After adding 3 liters of water, the new ratio of milk to water becomes 3:5. Therefore, we can set up the equation:
\[ \frac{3x}{4x + 3} = \frac{3}{5} \]

**Step 5: Cross-multiply to solve for \( x \).**
Cross-multiplying gives us:
\[ 3 \cdot (4x + 3) = 5 \cdot 3x \]
Expanding both sides:
\[ 12x + 9 = 15x \]

**Step 6: Rearrange the equation to isolate \( x \).**
Rearranging the equation gives:
\[ 15x - 12x = 9 \]
\[ 3x = 9 \]
Dividing both sides by 3:
\[ x = 3 \]

**Step 7: Calculate the initial quantity of milk.**
Now that we have \( x \), we can find the initial quantity of milk:
\[ \text{Initial quantity of milk} = 3x = 3 \times 3 = 9 \text{ liters} \]

**Final Answer:**
The initial quantity of milk is **9 liters**.

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